In a December document first reported by ProPublica, the Department of Justice argued that inquiring about citizenship status in the decennial census was critical to enforcing Section 2 of the Voting Rights Act, which protects against racial discrimination in voting. Measuring the total number of citizens of voting age in a region is vital to understanding voting rights violations, the department argued.

On Monday, 19 Democratic and independent state attorneys general and one governor, John W. Hickenlooper of Colorado, sent a 10-page letter to Commerce Secretary Wilbur Ross, who oversees the Census Bureau, arguing that the change to the census could “risk an unconstitutional undercount.” The decennial census has not had a citizenship query since 1950, they said.

And, they argued, “adding a citizenship question at this late date would fatally undermine the accuracy of the 2020 census, harming the states and our residents.”

The Justice Department is standing by its request.

“The Justice Department is committed to free and fair elections for all Americans and has sought reinstatement of the citizenship question on the census to fulfill that commitment,” a Justice Department spokesman, Devin M. O’Malley, said in a statement.

Even without the citizenship question, minorities have been undercounted in the national census, with undocumented immigrants and their legal relatives among the least responsive. Amid a fiery immigration debate — including Immigration and Customs Enforcement raids nationwide — the inclusion of a citizenship inquiry could make it worse.

“It’s all about trust,” said Mr. Hunter, who earlier in his career oversaw confidentiality policy at the C.D.C.’s National Center for Health Statistics. “The government is legally bound not to reveal the identities of individuals who participate — and yet at a time like this, you would need the individual to believe that.”

When census results are released, scientists often measure the impact of a disease by comparing its prevalence to the total population. With skewed census data, public health officials may invest in solving a problem that does not exist — or worse, may overlook one that does.

“This is completely foundational,” said Michael Fraser, the executive director of the Association of State and Territorial Health Officials. “We take for granted that we have a really accurate understanding of who lives in this country: their ages, ethnicities, where they live.”

Dr. Fraser added, “The bottom line is, if we are handed baseline numbers that aren’t accurate, everything we do for program planning and what we do for implementation will be inadequate.”

Public health officers use demographic data to model neighborhoods before launching preventive programs, like tracking old housing in low-income communities where they expect to find lead-based paint. The same is true for preventing asthma, a condition often correlated with substandard housing. By targeting the right homes for remediation early, officials can prevent disease and save millions of public dollars in treatment down the line.

The results of the census determine how more than $600 billion is appropriated across state and local governments each year, including federal block grants for children’s health and preventive care services. An immigrant-heavy region that underreports its total population could lose public health dollars — as well as funding for food programs, school programs and transportation services.

“It’s not as if immigrants going into the woodwork would solely harm services for that group. It would throw the whole system off,” said Dr. Georges C. Benjamin, the executive director of the American Public Health Association. “A representative census is what’s best for everyone.”

“Only U.S. citizens should be represented in Congress,” he said Tuesday. “If we counted only citizens for redistributing seats, California would give up several congressional seats to states that actually honor our Constitution and federal law.”

The top two Census Bureau seats have interim occupants, and financial constraints have led the bureau to skip two of its three trial runs of its overhauled process for 2020. Experts worry that the funding constraints will hinder the bureau’s ability to adjust the data for low participation rates or deploy adequate enumerators to low-response communities.

“Attorneys from the Department of Commerce are currently examining the justification for the data needed by the Department of Justice,” Albert E. Fontenot Jr., the associate director for decennial census programs at the Census Bureau, said in a briefing last month. “Technical experts at the Census Bureau are also looking at the issues.”